1. Don't out anyone... period
This needs no further information but remember outing not only shows a lack of trust but can affect a persons employment, relationships, family,... the list goes on and on. The general rule is, if the person says it is ok to talk about their transition with others that is one thing, if not then don't.
2. Don't ask what someone's old name was or worse what their "real" name is
Just don't... If a trans person want to volunteer this info let them do so on their own. They are who they are right now. Similarly, avoid asking to see pictures or asking any details about who they were before they transitioned. This also goes for someones genitals. Personally if you are concerned with what I have between my legs be either be on a date that is going well or you are my doctor. Everyone else can bugger off.
3. Don't assume you know a persons sexual identity based on the gender identity
This is one I get a lot actually. people assume a lot that I like men when in fact I identify more as a lesbian. Gender and sexuality are very different!
4. If you do not know someone's gender identity listen to them, ask.
I am trans, I make mistakes in this regard as well. It is not always cut and dry what pronouns to use when talking. I find the best approach is to listen to them for a bit using their name. If I cannot figure it out through context I ask.
5. Listen and be a friend
Understand that coming out is hard and stressful. It is not an easy thing to do and not the same as coming out as gay, lesbian or bi. Also many trans people experiment with their identity, I know I do. Be patient with them and most important be supportive. Remember there is no right way to transition or present a gender (or no gender). Not ever trans woman is femme and not every trans man is masculine. I for one fluctuate between full on female femme to androgynous even into gender queer maleness.
One other bit of advice that falls under this headline is to avoid giving tips that sound like compliments. Statements like "You look like a real girl" or "I'd never had known", etc. sound supportive but can be taken very badly. Instead tell the person simply that they look nice. Also comments like "When you were..." can be awkward at best. Other phrases that can get tricky include phrases that start with "biological...", and "genetic...". The gist is try to avoid questions and comments that can be construed as invalidating.
6. Help your friends feel included and support their fight for inclusion in public spaces
Even things as trivial as using public restrooms can be dangerous sometimes for trans people. The best way you can help in this regard is to support our fight for inclusive spaces and non-discrimination laws.
7. Words like "tranny," "shemale," "he-she,", etc...
Just don't use them...